1. These people are not idiots (at least the YECs aren't, I can't speak for the flat-earthers) and to dismiss them as idiots who will just go away is a serious mistake. They are very good at presenting convincing-sounding arguments, and refuting them can actually be quite challenging.
2. The root of their reasoning is a tacit acceptance of teleology, which cannot be logically refuted. They approach existential questions with the assumption that there has to be some kind of point to existence, some transcendent meaning or purpose. If you accept this premise, then there is actually a logically defensible line of reasoning that leads you to Christianity and thence to the inerrancy of the Bible, and thence to YEC (and even a flat earth if you're really being intellectually honest!) A failure to appreciate this is IMHO one of the reasons that the secular world is having such a hard time effectively resisting these movements. A life without purpose makes no sense to these people, just as a theory at odds with the data makes no sense to someone with a scientific mindset. So if science leads you to the conclusion that life has no transcendent purpose (and it does) then, on their world-view, science must be wrong, full stop. No amount of data is going to persuade them otherwise.